The ability to react to certain proteins in an allergic way is passed on from parents to their children, but a specific allergy is not.

So if a mom is allergic to pollen and the dad is allergic to fire ants, their child may develop allergies but it may be to a food instead. If 1 parent has allergies, the child is 50% likely to develop allergies, but it's a 75% chance if both parents are allergic.

In brief:
Not exactly

The ability to react to certain proteins in an allergic way is passed on from parents to their children, but a specific allergy is not.

So if a mom is allergic to pollen and the dad is allergic to fire ants, their child may develop allergies but it may be to a food instead. If 1 parent has allergies, the child is 50% likely to develop allergies, but it's a 75% chance if both parents are allergic.
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The exception, which is a controversial topic, is drug allergies, but this is usually dependent on metabolism of the drug which is inherited rather than the allergy.
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